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Wavelet Sets and Scaling Sets in Local Fields

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Abstract

We provide characterizations of minimally supported frequency multiwavelets, multiwavelet sets, generalized scaling sets, and scaling sets in a local field of positive characteristic. We also construct examples of multiwavelet sets and wavelet sets. In particular, we construct examples of unbounded wavelet sets and show that the corresponding wavelets are not associated with multiresolution analyses.

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Acknowledgements

The author is thankful to the referee for making some useful suggestions which helped in improving the presentation of the article.

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  1. Statistics and Mathematics Unit, 203 B. T. Road, Kolkata, 700108, India

    Biswaranjan Behera

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  1. Biswaranjan Behera
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Correspondence to Biswaranjan Behera.

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Communicated by Veluma Thangavelu.

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Behera, B. Wavelet Sets and Scaling Sets in Local Fields. J Fourier Anal Appl 27, 78 (2021). https://doi.org/10.1007/s00041-021-09887-2

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